Abstract
Panel data, which consist of observations on many individual units over two or more instances of time, have gradually become an important type of scientific data. Subsequently causal inference for panel data has attracted enormous interest from many fields as well as statistics. In this study, the rigorously formulated information flow analysis for time series, which is very concise in form and has been successfully applied in different disciplines, is generalized to identify the causality from homogeneous and independent identically distributed panel data. The resulting formula bears the same form as that for the former, though the meanings of the symbols differ. An algorithm is then proposed for panel data causality analysis, which has been validated with both linear and nonlinear problems. It has also been put to application to examine the causal relations among economic growth, energy consumption, trade openness, and energy price based on 15 Asian countries. Clearly identified are a strong bidirectional causality between economic growth and energy consumption, and a strong causality from import and export trade to economic growth. Energy price has no direct impact on energy consumption; it, instead, exerts a weak effect on the latter through influencing economic growth.
Highlights
In the past two decades, data have been accumulated at an exponential rate in essentially all fields, partly due to the easy access to social media and the interconnectivity of our society [1]
The above dynamical systembased formula may not be directly applicable. This is different from Granger causality, which is fundamentally a notion of probabilistic conditional independence, and can be applied to time series data and to crosssection and panel data [27]
All other causalities have not passed the significance test at the 85% confidence level, energy price has no direct causal relationship with either energy consumption or trade openness, though it does exert a limited impact on the economic growth
Summary
In the past two decades, data have been accumulated at an exponential rate in essentially all fields, partly due to the easy access to social media and the interconnectivity of our society [1]. Considering the success of the IF-based causality analysis for time series, we want to generalize it to panel data. The above dynamical systembased formula may not be directly applicable This is different from Granger causality, which is fundamentally a notion of probabilistic conditional independence, and can be applied to time series data and to crosssection and panel data [27]. The panel data set is generated with a one-way coupled anticipatory map This is a highly chaotic system designed by Hahs and Pethel [28] which fails the existing causal inference techniques : X1 (t + 1) = f (X1 (t)) , X2 (t + 1) = (1 − ε) f (X2 (t)) + εgα (X1 (t)) , (15). Though with a linear assumption, Algorithm-IF can capture the causality among an otherwise highly nonlinear panel dataset in a consistent way
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